108 



Professors Ayrton and Perry on 

 Fig. 1. 



t U i 



Values of a. 



for minimum error. But if we have used our material of 

 least resistance for the inner winding, b cannot in practice be 

 less than 0, for p cannot be less than p , and since r is never 

 less than 1, p would be some fraction of p if b were less than 

 0. Hence in practice we find that b must equal 0, that is, a 

 less heating-error is produced when all the wire is of copper than 

 when we use German-silver windings on the outside of the coil. 



IY. Making b equal to nought as the least value of b 

 attainable, we can now find the value of a to make the error 

 a minimum. To do this we must put b equal to nought, take 

 d equal to —1 in (9) , differentiate with respect to a, and equate 

 the result to 0. 



ThuS $(m)+0(n)-20te)=O, (18) 



where <j>(a) has the signification given to it in (17). 

 Since 6=0 



and d=—l 9 



it follows from (14) that 



m = 2-2a 



= -a j- 



= 2 -4a, -J 



(19) 



therefore, from (17) 



^(2-2a) + 0(-a)-2£(2-4a) = O. 



